The journalist took a short leave of absence from his BBC role after his wife died, but has since returned to work.

Ms Busby, a novelist, was a schoolfriend of Mr Peston's sister and the pair began dating when they were studying at different universities, although it was short-lived and ended when he took a posting in Brussels.

They later rekindled their relationship in the mid-1990s after her first marriage – from which she has a son, Simon – ended.

She told an interviewer in 2009 how they were brought back together when Mr Peston's sister was seriously injured in a road accident and suffered memory loss.

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She said: "I started going to see her with photographs to talk about our school days and help her piece her memory back together.

"Robert was often there at the same time, but I was feeling so low that I didn't think he – so handsome, so successful – could possibly be interested in me."

The couple have a teenage son, Max.

Peston later tweeted a picture of his late wife's engagement ring in the hope that someone may recognise it.

He wrote: "Here are my late wife's stolen engagement ring and wedding band. A bit blurred but perhaps someone will spot them."

The BBC journalist said: "The loss of my late wife's engagement, wedding and Cariad rings is desperately upsetting for me and our two sons.

"I had hoped to pass them on to the boys.

"If anyone knows anything about their whereabouts, I would be so grateful."